Absolutely Small - Michael D. Fayer [132]
FIGURE 19.6. Schematic of the band structure of a semiconductor. The valence band is essentially filled. The gap in energy to the next band is relatively small. Some electrons are thermally excited above the Fermi level into the conduction band.
Thermal Energy Affects Electrical Conduction in Metals
Thermal energy is necessary in semiconductors to generate conduction electrons. Thermal energy also strongly influences electrical conduction in metals, although thermal energy is not necessary to generate the conduction electrons. In a piece of metal wire connected to a battery, there are electrons moving toward the positive end. As electrons leave the wire, they are replenished by electrons entering from the negative side of the battery. Current (electrons) flowing through a piece of wire will cause its temperature to rise. The heating elements in an electric stove or an electric space heater get very hot from a large current flowing through them. They get so hot that they glow red. The red color is black body radiation from the hot metal. We have said that electrons can readily flow through a piece of metal because the electrons are in delocalized MOs that span the metal. It only requires an electric field (connection to a battery or other voltage source) to get them moving in a particular direction. So the question is why does the flow of electrons cause the metal to heat up?
The electrons in a metal should be thought of as wave packets that are more or less localized. We discussed wave packets in Chapter 6 in connection with the Heisenberg Uncertainty Principle. The electron wave packets in a metal are formed from superpositions of the delocalized electronic MO wavefunctions in a manner analogous to photon wave packets or electron wave packets in a vacuum that are superpositions of the delocalized momentum states. Electrons are negatively charged so an electron wave packet carries a negative charge. The electron is accelerated toward the positive end. The acceleration gives the electron increased kinetic energy.
Vibrations of a Solid Are Phonons
In Chapter 17, we briefly discussed the quantized vibrations of molecules in connection with the greenhouse gas, carbon dioxide. A piece of metal, which is made up of atoms, also has quantized vibrations. The atoms in a metal crystal lattice can jiggle around in their positions. Although they jiggle, an atom remains in the same spot on average. The motion of each atom is connected to the motions of the other atoms in the same manner that the motions of the atoms of a CO2 molecule are connected to each other (see Figure 17.2). CO2 has several distinct vibrations, symmetric and antisymmetric stretches, and two bending modes. These three different types of modes have vibrational energies (frequencies) that are very different from each other.
In a metal crystal lattice, each atom can move in all three dimensions. For N atoms, there are 3N lattice vibrations, where again, N is the number of atoms in the piece of metal. For any finite size piece of metal, this huge number of vibrations results in a band of vibrations rather than several discreet frequencies. At low temperature, only the lowest energy part of the band of vibrations is thermally excited. At higher temperature more lattice vibrations are excited and higher energy vibrations are excited. The excited vibrations have kinetic energy. The energy of the excited vibrations is what we think of as heat.
The quantized vibrations of a lattice are called